As promised (and late like often) - pictures. I have many of the needed parts, but it's been a ways down in the queue. Have barely started - have overhauled the front hub, and not much else. Hopefully over this winter...

Photos of the Raleigh Gazelle

I'm presuming from the hub that this is a 1939 - which is what the person (quite knowledgeable) I got this from told me.

I love the crusty look of the bike just as it is, but I admit, if it were mine, I would be cleaning it all up, at least with an oily rag.

I have never understood the use of the bolted-on seat stays. In fact looking at most of these older roadster types, it is more "screwed-on", the lower fasteners being pretty small.
Was the bolted-on seat stay a removable part for some stage in maintenance? Like removing the chain without a chain breaker?

I love the crusty look of the bike just as it is, but I admit, if it were mine, I would be cleaning it all up, at least with an oily rag.

I have never understood the use of the bolted-on seat stays. In fact looking at most of these older roadster types, it is more "screwed-on", the lower fasteners being pretty small.
Was the bolted-on seat stay a removable part for some stage in maintenance? Like removing the chain without a chain breaker?

I'm not really certain about the seat stays. Possibly it just made it easier to manufacture.

My plan is to clean it up, replace the tubes and tires, de-rust where it has rust, make the brakes functional, replace the handgrips, and do whatever else it takes to make it functional and reasonably safe. I might try to take a couple dents out of the fenders, and try to make the paint look better (gentle polishing), but I see no point in trying to make it look like new. I have all the parts I think I need, save some proper cotters for the crank arms.

Yup, chain removal. I haven't had a full chainguard on one of these but I've had one on a 26" Raliegh Sport. It didn't have the removable chainstays.
I've had 4 of these darn things and they all came with the hockey sticks. Actually, one came with the full chainguard but the previous owner kept it. I've never seen a 28" chainguard up close.
Once you start polishing, you won't be able to stop. It's going to look great. The stainless spokes on these really polish up nice and the old SA hubs have a different level of craftsmanship in the polishing and chroming that they blew off as time went on.